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|Singular Terms||I 147
Singular Term/Field: since an expression does not denote, it does not prevent it from being a real singular term. - e.g. "the number 4"/Field: does not denote any object. - But even with real singular terms, the question is whether the corresponding theorem is true. - The fact that a predicate has no extension does not prevent it from being a sortal: E.g. Homer E.g. "natural number". - FregeVsField: no singular term can stand for a concept. - (Wright pro Frege).
Sortal/Wright: syntactically, you cannot create statements of identity that contain a sortal like "well-being" (from "the well-being of children").
Singular: E.g. "2" in "2 + 3 = 5" - different: "there are two apples in the room": no singular term, but part of a quantifier - analyzed: numeric functor "the number of" plus singular term "three".
If "the direction of c1 = direction of c2" - logically equivalent: "c1 and c2 are parallel" - then expressions like "the direction of" cannot function semantically as a singular term. - If syntactically and semantically singular term, then they are without ontological commitment to other entities than lines. (no direction(s)).
Singular term/Field: we reject a singular term like e.g. "87" - solution: quantifier E87: "there are exactly 87" - quantifiers are not singular terms.
"87" does not appear as a name but as part of an operator.
Realism, Mathematics and Modality Oxford New York 1989
Truth and the Absence of Fact Oxford New York 2001
Science without numbers Princeton New Jersey 1980